SU-F-J-79: Extension of Fixed-Point Iteration Algorithm for Inverse Deformation

2016 ◽  
Vol 43 (6Part9) ◽  
pp. 3424-3424 ◽  
Author(s):  
M R Anders ◽  
M Chen ◽  
S Jiang ◽  
W Lu
Keyword(s):  
Fixed Point ◽  
Iteration Algorithm ◽  
Fixed Point Iteration ◽  
Inverse Deformation

A Fixed-Point Iteration Method With Quadratic Convergence

2012 ◽  
Vol 79 (3) ◽  
Author(s):  
K. P. Walker ◽  
T.-L. Sham
Keyword(s):  
Fixed Point ◽  
Nonlinear Equations ◽  
Unit Root ◽  
Iteration Method ◽  
Equation System ◽  
Higher Order ◽  
Iteration Algorithm ◽  
System Of Nonlinear Equations ◽  
Fixed Point Iteration ◽  
Root Functions

The fixed-point iteration algorithm is turned into a quadratically convergent scheme for a system of nonlinear equations. Most of the usual methods for obtaining the roots of a system of nonlinear equations rely on expanding the equation system about the roots in a Taylor series, and neglecting the higher order terms. Rearrangement of the resulting truncated system then results in the usual Newton-Raphson and Halley type approximations. In this paper the introduction of unit root functions avoids the direct expansion of the nonlinear system about the root, and relies, instead, on approximations which enable the unit root functions to considerably widen the radius of convergence of the iteration method. Methods for obtaining higher order rates of convergence and larger radii of convergence are discussed.

Structural Analysis Methods for Differential Algebraic Equations via Fixed-Point Iteration

2016 ◽  
Vol 13 (10) ◽  
pp. 7705-7711 ◽  
Author(s):  
Juan Tang ◽  
Wenyuan Wu ◽  
Xiaolin Qin ◽  
Yong Feng
Keyword(s):  
Fixed Point ◽  
Structural Analysis ◽  
Iteration Method ◽  
Large Scale ◽  
Complexity Analysis ◽  
Differential Algebraic Equations ◽  
Iteration Algorithm ◽  
Algebraic Equations ◽  
Fixed Point Iteration ◽  
Dae Systems

Motivated by Pryce’s structural analysis method for differential algebraic equations (DAEs), we show the complexity of the fixed-point iteration algorithm (FPIA) and propose a fixed-point iteration method with parameters. It leads to a block fixed-point iteration method (BFPIM) which can be applied to immediately calculate the crucial canonical offsets for large-scale (coupled) DAE systems with block-triangular structure, and its complexity analysis is also given in this paper. Moreover, preliminary numerical experiments show that the time complexity of BFPIM can be reduced by at least O(l) compared to the FPIA.

scholarly journals A New Approach To Solve Fuzzy Non-Linear Equations Using Fixed Point Iteration Algorithm

2013 ◽  
Vol 32 ◽  
pp. 15-21
Author(s):  
Goutam Kumar Saha ◽  
Shapla Shirin
Keyword(s):  
Fixed Point ◽  
Linear Equation ◽  
Graphical Representation ◽  
Linear Equations ◽  
Approximate Solutions ◽  
Iteration Algorithm ◽  
Fixed Point Iteration ◽  
New Approach ◽  
Non Linear Equation ◽  
Non Linear

A non-linear equation over linear fuzzy real numbers is called a fuzzy non-linear  equation. In Classical Mathematics a non-linear equation can be solved by using  different types of numerical methods. In this paper a new approach has been  introduced to get approximate solutions with the help of Fixed Point Iteration  Algorithm. Graphical representation of the solutions has also been drawn so that  anyone can achieve the idea of converging to the root of a fuzzy non-linear equation. DOI: http://dx.doi.org/10.3329/ganit.v32i0.13641 GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 32 (2012) 15 – 21

scholarly journals An alternating iteration algorithm for solving the split equality fixed point problem with L-Lipschitz and quasi-pseudo-contractive mappings

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Meixia Li ◽  
Xueling Zhou ◽  
Haitao Che
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Split Feasibility Problem ◽  
Fixed Point Problem ◽  
Feasibility Problem ◽  
Iteration Algorithm ◽  
Point Problem ◽  
Contractive Mappings ◽  
Common Fixed Point Problem ◽  
Significant Generalization

Abstract In this paper, we are concerned with the split equality common fixed point problem. It is a significant generalization of the split feasibility problem, which can be used in various disciplines, such as medicine, military and biology, etc. We propose an alternating iteration algorithm for solving the split equality common fixed point problem with L-Lipschitz and quasi-pseudo-contractive mappings and prove that the sequence generated by the algorithm converges weakly to the solution of this problem. Finally, some numerical results are shown to confirm the feasibility and efficiency of the proposed algorithm.

scholarly journals The iterative solutions of split common fixed point problem for asymptotically nonexpansive mappings in Banach spaces

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yuanheng Wang ◽  
Xiuping Wu ◽  
Chanjuan Pan
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Optimization Problems ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Iteration Algorithm ◽  
Point Problem ◽  
Asymptotically Nonexpansive ◽  
Split Common Fixed Point

AbstractIn this paper, we propose an iteration algorithm for finding a split common fixed point of an asymptotically nonexpansive mapping in the frameworks of two real Banach spaces. Under some suitable conditions imposed on the sequences of parameters, some strong convergence theorems are proved, which also solve some variational inequalities that are closely related to optimization problems. The results here generalize and improve the main results of other authors.

scholarly journals Differentiable Forward and Backward Fixed-Point Iteration Layers

IEEE Access ◽  
2021 ◽  
Vol 9 ◽  
pp. 18383-18392
Author(s):  
Younghan Jeon ◽  
Minsik Lee ◽  
Jin Young Choi
Keyword(s):  
Fixed Point ◽  
Fixed Point Iteration
Sign in / Sign up

Export Citation Format

Share Document